I am attempting to model a situation with a second order differential equation. The model appears to be valid, and all units match up properly. The problem, however, is that my resulting equation is autonomous to the independent variable. How do I figure out my units of time, or if they aren't in the system, how do I put them there? (Equations to follow)

Question

anonymous · Answer

It's system , I assume?

anonymous · Answer

$$x''=\frac{V_t P_0 R_b ^2 \pi}{M_D (V_t +R_b ^2 \pi x)}=\frac{c}{x}$$

anonymous · Answer

Third part should be $$\frac{c}{a+bx}$$

anonymous · Answer

No, it is not a system. Just one equation. My goal is to find x' at a given time. The equation can be solved easily, but there is no indication on thee units of time in the result.